Please provide details. Are these POP accounts or IMAP? Are both accounts being updated or just one?

There is only one account, and it's IMAP.

Also, how do I have Thunderbird delete the messages it has downloaded from the AOL web site?

I'm still confused. You originally stated you wanted to combine accounts and now you state you want to delete messages. Maybe if you write a paragraph to explain what you have and what you would like the results to be it would help. Thanks much.

I have one mail account on AOL. But I have one old account and one new account in Thunderbird on my PC for that one AOL account. I want to combine the two Thunderbird accounts. I don't want to lose the old emails; I want both old and new emails to appear in just under just one heading in Thunderbird.

I have an additional problem that I just discovered that Thunderbird is not deleting the messages on the web once they have been downloaded to Thunderbird. I don't want my emails to be in 2 places.

My first question had only one problem, but I have added an additional problem.

If an account is POP, it can delete from server on download. IMAP accounts do not do that. Some clarification in that is needed.

You said you had one account and it is IMAP. You also stated two accounts on Thunderbird for same email account. Are they both IMAP or POP? With clarification, we can address this. Your posts imply three accounts and I am trying to understand that.

My account in Thunderbird is connected to AOL Mail and has been IMAP for years, but apparently, at one time, downloaded messages were deleted from the web. The oldest email in the inbox on the web is 11/4/2024. which is about the time that Thunderbird and AOL quit communicating. Thunderbird has been my primary interface to AOL for years, and I've never cleaned out the inbox on the web. Either Thunderbird or AOL changed in early November 2024. For years I've also gotten a message, when I opened Thunderbird, that the app could not connect to the IMAP server, but it all seemed to work. It seems that what you're telling me is that if I want the messages to be deleted on the web after download, I need to change the settings in Thunderbird to POP. If so, then how do I do that?

There is only one email service -- AOL Mail. Thunderbird is connected only to AOL Mail. I now have 2 sets of inboxes in Thunderbird that I want to combine. What do you define as "account"?